La meva germana surt de casa sense paraigua i arriba tard a la feina.

In standard Catalan, a definite article is usually used before a possessive:

• la meva germana = my sister
• el meu pare = my father
• la seva amiga = his/her friend

So this is the normal pattern. English does not use an article here, but Catalan usually does.

There are some cases where the article can be omitted, but for a learner, la meva germana is the safe and standard form.

Surt is the 3rd person singular present of sortir.

So:

• jo surto = I go out / I leave
• tu surts = you go out / leave
• ell/ella surt = he/she goes out / leaves

In this sentence, surt de casa means leaves home or goes out of the house/home.

Because casa without an article often means home in Catalan.

• sortir de casa = to leave home
• ser a casa = to be at home
• tornar a casa = to return home

If you say de la casa, it sounds more literal: out of the house/building. So:

• de casa = home, in a general personal sense
• de la casa = from the house, more specifically the building

After sense (without), Catalan often leaves out the article when talking about something in a general or indefinite way.

• sense paraigua = without an umbrella
• sense diners = without money
• sense cotxe = without a car

You can also hear:

• sense un paraigua = without an umbrella, with a bit more emphasis on one
• sense el paraigua = without the umbrella, meaning a specific one

So sense paraigua is very natural here.

Paraigua is usually masculine:

• el paraigua = the umbrella

This can surprise learners because it ends in -a, but its gender is still masculine. In your sentence, you cannot see the gender directly because there is no article before it.

Arriba is the 3rd person singular present of arribar:

• jo arribo = I arrive
• tu arribes = you arrive
• ell/ella arriba = he/she arrives

Here it matches the same subject, la meva germana.

Because Catalan does not need to repeat the subject if it is already clear.

So this is perfectly normal:

• La meva germana surt de casa sense paraigua i arriba tard a la feina.

The subject la meva germana applies to both verbs:

• she leaves home
• and she arrives late to work

Repeating it would usually sound unnecessary:

• La meva germana surt de casa sense paraigua i la meva germana arriba tard...

That is grammatical, but not natural unless you want extra emphasis.

Because tard is an adverb, and with arribar the normal expression is:

• arribar tard = to arrive late

So:

• arriba tard = she arrives late

This is just the usual word order. Also, tard does not change for gender or number.

Because arribar normally takes the preposition a when you say where someone arrives:

• arribar a casa
• arribar a l’estació
• arribar a la feina

Here, feina is feminine singular, so:

• a + la feina = a la feina

If the noun were masculine singular with el, you would usually get a contraction:

• a + el treball → al treball

But with la, there is no contraction:

• a la feina

It can mean either, depending on context.

• arribar tard a la feina usually means to arrive late for work / at work
• tenir molta feina means to have a lot of work

So feina can refer to:

• work in general
• someone’s job
• the place where they work, depending on the sentence

In this sentence, it naturally means work in the sense of her workplace/job.

The present tense in Catalan can do both.

So this sentence could mean:

• a habit/routine: your sister typically leaves home without an umbrella and arrives late for work
• a vivid present narration: this is what is happening in the story right now

Without extra context, both readings are possible. Catalan, like English, often uses the present tense this way.